新方法让降维模型更准，提升两倍精度。
Operator Inference Aware Quadratic Manifolds with Isotropic Reduced Coordinates for Nonintrusive Model Reduction
- 贪心训练同时优化数据重建与降维模型预测误差
- 在流体问题中使降维模型精度提高达100倍
- 适合需要高精度非侵入式建模的工程仿真场景
传统二次流形用于非侵入式降维建模时，通常仅最小化快照数据的重构误差，忽略了下游学习阶段中降维模型的预测误差。本文提出一种贪心训练策略，同时考虑快照数据的重构误差和基于嵌入数据训练的降维模型的预测误差。由于该方法旨在获得高精度的降维模型，能避免导致建模困难的振荡或非光滑嵌入。在传输和湍流流动问题上的数值实验表明，采用所提贪心方法训练的二次流形，其生成的降维模型精度相比仅以重构误差为目标训练的流形高出多达两个数量级。
原文摘要 · Abstract (English)
Quadratic manifolds for nonintrusive reduced modeling are typically trained to minimize the reconstruction error on snapshot data, which means that the error of models fitted to the embedded data in downstream learning steps is ignored. In contrast, we propose a greedy training procedure that takes into account both the reconstruction error on the snapshot data and the prediction error of reduced models fitted to the data. Because our procedure learns quadratic manifolds with the objective of achieving accurate reduced models, it avoids oscillatory and other non-smooth embeddings that can hinder learning accurate reduced models. Numerical experiments on transport and turbulent flow problems show that quadratic manifolds trained with the proposed greedy approach lead to reduced models with up to two orders of magnitude higher accuracy than quadratic manifolds trained with respect to the reconstruction error alone.
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